Abstract
We present a necessary and sufficient condition for a spinor \({\omega}\) to be of nullity zero, i.e. such that for any null vector v, \({v \omega \neq 0}\) . This dives deeply in the subtle relations between a spinor \({\omega}\) and \({\omega_c}\) , the (complex) conjugate of \({\omega}\) belonging to the same spinor space.
Similar content being viewed by others
References
Batista C.: Pure subspaces, generalizing the concept of pure spinors. J. Geom. Phys. 81, 117–127 (2014)
Budinich, M.: On computational complexity of Clifford algebra. J. Math. Phys. 50(5), 053514 (2009). arXiv:0904.0417 [math-ph]. 2 April 2009
Budinich M.: The extended fock basis of Clifford algebra. Adv. Appl. Clifford Algebras 22(2), 283–296 (2012)
Budinich M.: On spinors and null vectors. J. Phys. A Math. Theor. 47(11), 115201 (2014)
Budinich P., Trautman A.M.: The Spinorial Chessboard. Trieste Notes in Physics. Springer, Berlin (1988)
Budinich P., Trautman A.M.: Fock space description of simple spinors. J. Math. Phys. 30(9), 2125–2131 (1989)
Cartan É.: Les groupes projectifs qui ne laissent invariante aucune multiplicité plane. Bulletin de la Société Mathématique de France 41, 53–96 (1913)
Cartan, É.: The Theory of Spinors. Hermann, Paris (1966). (first edition: 1938 in French)
Charlton, P.: The Geometry of Pure Spinors, with Applications. PhD thesis, University of Newcastle (N.S.W.), Department of Mathematics (1997)
Chevalley C.C.: Algebraic Theory of Spinors. Columbia University Press, New York (1954)
Kopczyński, W.; Trautman, A. M.: Simple spinors and real structures. J. Math. Phys. 33(2), 550–559. 1992 (with thanks to the anonymous referee for suggesting this paper)
Pavšič M.: Space inversion of spinors revisited: a possible explanation of chiral behavior in weak interactions. Phys. Lett. B. 692(3), 212–217 (2010)
Trautman A.M., Trautman K.: Generalized pure spinors. J. Geom. Phys. 15(1), 1–22 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Budinich, M. On Spinors of Zero Nullity. Adv. Appl. Clifford Algebras 25, 771–786 (2015). https://doi.org/10.1007/s00006-015-0547-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00006-015-0547-8